Identifying unique sets of combinations

We have a table as part of our HR system that is used to categorize days off. For example, "S" (for sick) is in the SCKAC, USEDS, VACCK and 14 other categories (I know, I know). V(acation) is in 7 categories, and so on. These things are categorized in such a way because they intersect so much. For example, a Carry-over vacation day and a Vacation day each have the same effect in terms of Vacation Balance, but very different effects when it comes to calculating next year's new balance.

In all, there are 110 absence codes that are grouped into 55 different categories. In an effort to simplify all of this, I've been asked to identify categories that share common members, with no exceptions. (In other words, if categories AAA, ABB and ACC all contain V and C, and none of them contain anything else, they are exact duplicates.)

By the same token, If V and G are in 5 categories, but a sixth category lacks G, the powers that be would like this noted also.

I'm sure there's a way to get to this answer and still maintain what's left of my sanity (many of you realize that there's little left), but I have not yet landed on it. I thought SQL might get me to the answer most readily, but try as I might I haven't found a workable solution yet; my CTEs quickly get too complex for me to follow. (See prior note on sanity.) Pivot table doesn't seem quite right (though it may help); counts are not definitive enough...

So I thought I'd come to this group; see if you've had a similar situation, and might be willing to share how you arrived at a solution.

Thanks!
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